Math 9R: Integrated Algebra Curriculum - Quia



Math 9R: Integrated Algebra Curriculum

Semester 1

Unit 1: Trigonometry & Pythagorean Theorem

• Find sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides

• Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle

• Find the measure of an angle of a right triangle, given an acute angle and length of another side

• Word Problems using trigonometric functions, including angle of elevation and angle of depression.

• Determine the measure of a third side of a right triangle using the Pythagorean Theorem, given the length of any two sides

Unit 2: Number System, Sets, Venn Diagrams, & Operations

1. Number System

• Classify numbers to given sets (rational, irrational, natural, integer, whole)

• Identify and apply properties of real numbers (closure, commutative, associative, distributive, identities, inverses)

2. Sets

• Use set-builder notation to illustrate the elements of a set, given elements in roster form

• Use interval notation to illustrate the elements of a set, given elements in roster form

• Find the complement of a subset of a given set, within the universe

• Find the intersection of sets (2 or 3 sets)

• Find the union of sets (2 or 3 sets)

• Graph compound inequalities

3. Venn Diagrams

• Use a Venn diagram to support logical reasoning, word problems (2 and 3 circles)

• Interpret Venn diagram and shade

• Show intersection, union, complement of sets in a Venn diagram

4. Operations

• Evaluate expressions using order of operations

• Evaluate expressions involving absolute value, and exponents

• Understand and use scientific notation to compute products and quotients of numbers

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Unit 3: Monomials and Polynomials

• Multiply and divide monomials expressions with a common base, using the properties of exponents

• Add, and subtract, and multiply monomials and polynomials

• Multiply a monomial by a polynomials, and a polynomial by a polynomial when the leading coefficient is any rational number

• Divide a polynomials by a monomial

• Divide a polynomial by a binomial (long division) where the quotient has no remainder

Unit 4: Equations and Inequalities

• Solve multi-step equations

• Solve multi-step inequalities

• Transform literal equations

• Translate verbal phrase into an algebraic expression

• Write a verbal expression that matches a given mathematical expression

• Translate verbal sentences into mathematical equations or inequalities

• Distinguish between an algebraic expression and an algebraic equation

• Write algebraic equations or inequalities the represents a situation

• Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

o Coin, consecutive integer, perimeter, investment, ratio, distance

• Solve algebraic problems arising form situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation

Unit 5: Functions (Math 8 & 9R)

• Define and use correct terminology when referring to functions (domain and range)

• Describe a situation involving relationships that matches a given graph

• Interpret a graph, and explain

• Determine if a relation is a function, by examining ordered pairs in a table and inspecting graph (vertical line test)

• Interpret multiple representations using equation, table of values, and graph

• Find a set of ordered pairs to satisfy a given linear numerical pattern (expressed algebraically); then plot the ordered pairs and draw the line (Given table, fill out, write equation, graph line)

Unit 6: Graphing

LINES

• Graph a line using a table

• Determine whether a given point is on a line, given the equation

• Explain slope as a rate of change between dependent and independent variable

• Determine the slope of a line given the coordinates of two points on a line

• Graph a line using slope-intercept form

• Determine the slope of a line, given its equation in any form

• Write the equation of a line given the slope and coordinates of a point on the line

• Write the equation of a line given its slope and the coordinated of two points on the line

• Write the equation of a line parallel to the a line or the x and y axes

• Determine if two lines are parallel, perpendicular, given the equations in any form

• Graph a system of linear equations

• Solve a system of equations algebraically using substitution method, and addition

• Analyze and solve verbal problems whose solution requires solving a system of linear equations in two variables

INEQUALITIES

• Graph a linear inequality

• Graph a system of linear inequalities

• Determine whether a given point is in the solution set of a system of linear inequalities

ABSOLUTE VALUE

• Solve absolute value equations

• Graph an absolute value equation using a table

• Investigate how the graph changes using graphing calculator

EXPONENTIAL GROWTH AND DECAY

• Analyze and solve verbal problems that involve exponential growth and decay

Unit 7: Radicals

• Simplify radical terms (with and without variables in the radicand)

• Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form

• Rationalize the denominator

SEMESTER 2

Unit 8: Transformational Geometry (Math 8 topics)

• Describe and identify transformations in the plane using proper function notation (rotations, point reflections, reflections, translations, dilations)

• Draw the image of the figure under rotations of 90, 180, and 270

• Draw the image of a figure under a reflection over a given line

• Draw the image of a figure under a translation

• Draw the image of a figure under a dilation

• Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation

Unit 9: Geometry

ANGLES (Math 8 topic)

• Identify pairs of vertical angles as congruent

• Identify pairs of supplementary and complementary angles

• Calculate the missing angle in a supplementary or complementary pair

• Determine angle pair relationship when given two parallel lines cut by a transversal

• Calculate the missing angle measurements when given two parallel lines cut by a transversal

• Calculate the missing angle measurements when given two intersecting lines and an angle

AREA & PERIMETER

• Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle. (Irregular area and perimeter)

• Shaded area questions

• Use formulas to calculate volume of a rectangular prism, cylinder, cone, sphere, pyramid

• Use formulas to calculate surface area of rectangular solids and cylinders

Unit 10: Factoring (Math 8/9R topic)

• Factor algebraic expressions using the GCF

• Identify and factor the difference of two perfect squares

• Factor algebraic expressions completely, including trinomials with a leading coefficient of one or greater than one.

Unit 11: Algebraic Fractions

• Find value of a variable for which an algebraic fraction is undefined

• Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms

• Add or subtract fractional expressions with monomial or like binomial denominators

• Multiply and divide algebraic fractional expressions

• Solve fractional equations

Unit 12: Quadratics

• Solve Factorable Quadratics

• Understand and apply the multiplication property of zero to solve quadratics equations with integral coefficients and integral roots

• Understand the difference and connection between roots of a quadratic equation and factors of a quadratic equation

• Solve incomplete quadratics

• Analyze and solve verbal problems that involve quadratic equations

• Solve algebraic proportions in one variable which result in linear or quadratic equations

• Determine the vertex and axis of symmetry of a parabola, given its equation

• Determine the vertex and axis of symmetry of a parabola, given its graph

• Investigate and generalize how changing the coefficients of a function affects its graph

• Find the roots of a parabolic function graphically

• Solve systems of linear and quadratic equations graphically

• Solve a system of one linear and one quadratic equation in two variables, where factoring only is required

• Identify a graph linear, quadratic, absolute value, and exponential functions

Unit 13: Measurement

• Calculate rates using appropriate units (ex. rate of a spaceship versus the rate of a snail)

• Solve problems involving conversions within measurement systems, given the relationship between the units

• Precision and accuracy

• Calculate relative error in measuring square and cubic units, where there is an errir in the linear measure

Unit 14: Statistics

• Categorize data as qualitative or quantitative

• Determine whether the data to be analyzed is univariate or bivariate

• Determine when collected data or display of data may be biased

• Identify and describe sources of bias and its effect, drawing conclusions from data

• Compare and contrast the appropriateness of different measures of central tendency for a given data set

• Construct a histogram, cumulative frequency histogram, and box and whisker plot, given a set of data

• Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box and whisker plot

• Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot

• Find the percentile rank of an item in a data set and identify the point values for firstm second, and third quartiles

• Determine whether two sets of data show direct variation

• Create a scatter plot of bivariate data

• Identify the relationship between independent and dependent variables from a scatter plot (positive, negative, or none)

• Understand the difference between correlation and causation

• Identify variables that might have a correlation but not a causal relationship

• Construct manually a reasonable line of best fit for a scatter plot and determine the equation of the that line

• Evaluate published reports and graphs that are based on data by considering experimental design, appropriateness of the data analysis, and the soundness of the conclusions

• Students will make predictions that are based upon data analysis

• Recognize how linear transformations of one variable data affect the data’s mean, median, mode and range

• Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation

Unit 15: Probability

• Determine the number of possible events using the counting techniques or the Fundamental Counting Principle

• Determine the number of elements in a sample space and the number of favorable events

• Calculate the probability of an event and its complement

• Replacement and without replacement (conditional probability)

• Determine the number of possible arrangements of a list of items (permutations)

• Evalute expressions involving factorials

• Determine empirical probabilities based on specific sample data

• Determine, based on calculated probability of a set of events, if:

o Some or all are equally likely to occur

o One is more likely to occur than another

o Whether or not an event is certain to happen or not to happen

• Calculate the probability of:

o A series of independent events

o Two independent events

o Two dependent events

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